Determining that Trees have Value
Homeowners have long been interested in the way in which the presence of trees increases the perceived value of a property to homeowners, as evidenced by publications such as Brian R. Payne’s “The Twenty-Nine Tree Home Improvement Plan” (1973). This was one of the first articles that attempted to put a dollar value on urban trees. Payne declares that
The amenities provided by trees in residential neighborhoods are sufficiently sought after to make nurserymen a major influence on the metropolitan landscape. Shade, wind reduction, screens for privacy, an environment for wildlife, climbing areas for children, and natural beauty are the motivations behind the annual purchase of veritable forests by American homeowners.
In a short, two-page write-up for Natural History, Payne discusses an experiment in which a scale model house was appraised with varying quantities of trees “planted” on the model. As the title implies, he achieved the maximum addition of value with twenty-nine trees on a half acre lot, adding $4,300 to the property value.
This method of comparing similar houses with and without tree canopy continued to pervade attempts to value the influence of trees on residential prices. In 1980, another attempt to quantify the amenity value of trees was published in the Journal of Arboriculture. Dominic Morales’ “The Contribution of Trees to Residential Property Value” created pairs of sixty houses with “comparable” structural characteristics and compared those with and without substantial tree cover. A multiple regression was also used to control for variables available from the town assessor. Within this framework, the author determined that “good tree cover” added $2,686 (or 6% of total value) to the property’s value in this town (Manchester, Connecticut). However, no mention is made of the variance within this sample, and it is unclear whether these numbers bear much external validity. It does, however, represent an early determination that trees have measurable value to individual properties within the context of the housing market.
In a similar attempt was made by the US Forest Service in 1987, when Anderson and Cordell published “Influence of Trees on Residential Property Values in Athens, Georgia.” They focus on the inclusion of trees in the landscaping of a property, and whether that increases the sale price of that property. Anderson and Cordell assess tree canopy with a binary variable, considering only whether or not a property’s landscaping includes trees. In doing so, they find that the inclusion of trees in landscaping is correlated with a 3.5-4.5% increase in sales prices.
These studies form a starting point for my investigation, implying that there is a positive relationship between a house’s value and the presence of trees on that house’s property. Their analysis is limited, however, by the fact that they do not quantify the amount of tree canopy, only its presence or the lack thereof. Additionally, they do not consider possible “spillover effects,” where nearby tree canopy which is not on a property itself may still increase the value of that property—a case of external benefits.
I attempt to address these concerns with a hedonic analysis, which breaks down the value of a home into a function of its attributes. In doing so, I consider the proportion of an area covered by tree canopy to contribute to the price of a house, thereby giving an implicit price to tree canopy. An important difference considered in my analysis is the contribution of external benefits. I do so by using the block group as my basic unit of analysis. Although the ideal experiment would use the individual house as the basic unit and address external benefits with a given radius around each property, the block-group method provides a much more feasible and analytically-sound alternative.
Rosen: The Hedonic Approach
Sherwin Rosen (1974) provides the framework for hedonic analysis in his seminal 1974 paper, “Hedonic Prices and Implicit Markets.” This paper connects the utility-maximizing model to the empirical method of estimation, defining the hedonic hypothesis that “goods are valued for their utility-bearing attributes or characteristics.” Rosen’s model, therefore, begins by considering the value of any good as a function of its characteristics. By measuring the quantity of each characteristic contained in a good, one can calculate the implicit price of that characteristic.
Rosen’s theory is based on the idea of product differentiation. This means that for any class of product, there are variations on that product with differing quantities of its characteristics. These varied products also have different prices, as rational consumers operating in a purely competitive market will always choose the lowest-priced product with the highest-valued bundle of characteristics. This implies that marginal changes in one attribute of a good in equilibrium will produce a measurable effect on the price of that good. This effect is the correlation coefficient between a good’s price and the quantity of the characteristic of interest, and defines the implicit price of each included characteristic.
Ideally, Rosen’s theory could be tested by varying the quantity of one of a product’s characteristics, and observing the resultant change in price. However, in the absence of a practical means of performing such an experiment, we can approximate it by observing similar products with differing quantities of that characteristic, controlling for variation in other characteristics. Therefore, given a sufficient number of products with variable characteristics and different prices, we can compare the variations in product price to the differing quantities of its characteristics, and derive an implicit price for each.
Applying the Hedonic Method to Residential Amenities
Since its publication, many researchers have applied Rosen’s model to valuation of amenities available to homeowners via the housing market. An excellent example was published in the Journal of Urban Economics in March 2015. Yinger’s “Hedonic markets and sorting equilibria: Bid-function envelopes for public services and neighborhood amenities” applies a hedonic framework to a number of neighborhood amenities, including educational quality and distance to amenities such as lakefronts and airports. Although his analysis extends Rosen’s method to include consideration of the “envelope” of overlap in consumers’ bid functions for housing, his method represents a concrete application of the hedonic method in quantifying the value of residential amenities.
Gibbons, Mourato, and Resende also apply Rosen’s method to the valuation of many so-called natural amenities in their 2013 paper, “The Amenity Value of English Nature: A Hedonic Price Approach.” The authors assess the value to urban settings of nearby habitats, protected areas, urban parks and gardens, and similar amenities. Their analysis is extremely comprehensive, based on the theory that over large geographic areas, the interplay between several amenities of interest may have a non-zero effect on housing prices. In doing so, they consider both the proportion of several amenities located within a given ward (their sampling unit) and the distance to other amenities, such as coastline and national parks. They also control for a large number of potentially significant variables accounting for differential housing prices.
The authors conclude that many of their amenities significantly contribute to house price, especially nearby presence of wetlands, green space, and green belts (a land use policy which aims to retain forested or otherwise “green” areas around the circumference of a city). They report especially high levels of significance for London, suggesting that heavily urban areas may experience an especially high implicit price of open-space amenities. Although their analysis does not explicitly address tree canopy, they provide a useful template for application of the hedonic model.
Li, Saphores, and Gillespie not only apply the hedonic framework, but also use a data analysis method similar to my own in “A comparison of the economic benefits of urban green spaces estimated with NDVI and with high-resolution land cover data” (2014). The authors use hedonic analysis to estimate the value of neighborhood green space, and use an aerial land-cover classification technique to calculate the green space proportions within each of their sample areas (similar to the Maximum Likelihood Classification technique which I discuss in section 4.1). The authors’ focus in this paper is on the differing value of their two different resolutions of data which they collect—however, they do establish a correlation between price elasticity of housing and the presence of green space.
In this study, the authors find a weak relationship between housing prices and levels of nearby green space, notably to neighborhood parks. Though they do not provide a calculated implicit price, they do illustrate the value to hedonic modeling of a spatial approach, which intrinsically considers quantities of an amenity as well as its distribution. Their result on which they primarily focus is the value of high-resolution data over moderate-resolution data. Even so, they provide a contemporary example of a technique similar to that which I employ, and use that technique to model the hedonic approach in a way similar to what I accomplish.
Incorporating Willingness-To-Pay
Rosen’s method produces the implicit price of a good’s characteristics—that is, how much an increase in the quantity of that characteristic would increase the price of the good. However, if I want to determine the welfare gains to consumers from an increase of the quantity of that characteristic, I need to determine more information about their individual willingness-to-pay (WTP) for that characteristic. On a market scale, WTP for a characteristic is equal to its implicit price. On an individual level, however, WTP is determined by qualities of the consumer. This includes qualities such as income, education, and race. In other words, this asks “Given an implicit price for tree canopy, how much more canopy would a given consumer be willing to purchase given an increase in their income?” Other qualities of residents could, of course, be substituted for income in this statement.
This stage of experimentation is not frequently applied to hedonic analysis, but Kiel and Zabel do something similar in their 2001 paper, “Estimating the Economic Benefits of Cleaning Up Superfund Sites: The Case of Woburn, Massachusetts.” Their research uses a hedonic method to consider the value not of an environmental amenity, but of a disamenity: proximity to hazardous waste sites. Their analysis rests on the assumption that a site designated for cleanup on the National Priorities List lowers the value of nearby housing. In this case, the authors estimate consumer’s willingness-to-pay for the removal of the disamenity (i.e. the cleanup of the site).
Kiel and Zabel are interested in the amount households would be willing to pay for cleanup of the waste site. In this case, variable distance from the site allows the authors to segment their market and analyze the variable characteristics of each segment. Although Kiel and Zabel do not construct a WTP regression to account for the influence of each demographic characteristic on WTP, their framework could also be applied to include in this way, controlling for the fact that different demographic characteristics may reflect differing levels of WTP for cleanup.
Mahan, Polansky, and Adams, however, do apply the notion of variable willingness-to-pay to a hedonic regression in their 2000 paper, “Valuing Urban Wetlands: A Property Price approach.” In the paper, the authors apply a hedonic implicit price analysis similar to my own to estimate the value of proximity to wetland amenities. The authors analyze demand-shift variables in consumers, reflecting the notion that the preferences of the purchaser are theoretically determined by characteristics such as income, age, race, and ethnicity.
The authors segment their market based on distance from wetlands, and conduct a second-stage WTP regression based on a number of demand-shift variables. I will apply a similar method to my analysis, using demographic averages in each block group to determine variable willingness-to-pay. Because this will take the form of a regression of the implicit price of tree canopy on demographic characteristics, this will generalize the influence of each demographic characteristic on WTP as a whole.